Techniques and Methods 6-A19
U.S. GEOLOGICAL SURVEY
Techniques and Methods 6-A19
Historically, hydrologic processes that occur near the land surface, such as infiltration and evapotranspiration (ET) have been modeled separately from regional ground-water flow processes. Watershed-runoff models simulate near-surface hydrology and non-physically-based shallow unconfined ground-water flow, but rarely simulate physically-based three-dimensional regional ground-water flow. Similarly, regional ground-water modeling studies often simplify near-surface hydrologic processes such that recharge is specified to the model on the basis of external calculations independent of ground-water levels. Recently, however, regional ground-water flow models have been coupled to watershed-runoff models (Sophocleous and Perkins, 2000). Coupled models are used to simulate the effects of near-surface hydrology on regional ground-water flow by partitioning precipitation into various pathways among the atmosphere, surface, and subsurface. In this manner, recharge in regional ground-water models can be simulated in concert with changing climate. Moreover, ground-water flow and watershed-runoff modeling is improved by more realistically including the effects of ground-water seepage to land surface and streams, and by simulating the rejection of infiltration caused by high ground-water levels.
Modeling flow through the unsaturated zone has been a major obstacle to coupling watershed-runoff and regional ground-water flow models. One approach is to use Richards’ equation to model both saturated and unsaturated flow (Freeze, 1971). Richards’ equation is highly non-linear and more difficult to solve than the conventional ground-water flow equation. Models that incorporate Richards’ equation require much finer spatial grids and time steps, which limits their applicability for simulating regional ground-water flow problems. Additionally, modeling both saturated and unsaturated flow with the numerical solution of Richards’ equation requires that unsaturated flow be simulated in three dimensions, which is often unnecessary for basin-scale applications because the direction of unsaturated flow averaged over large grid cells is usually vertical (Mantoglou, 1992; Chen and others, 1994).
Another approach to coupling regional ground-water flow models to watershed-runoff models is to simulate unsaturated flow using Richards’ equation in only one dimension and three-dimensional ground-water flow. This approach has been used to model unsaturated flow over large areas (Pikul and others, 1974) and to develop the integrated surface-water and ground-water flow model MIKESHE (Refsgaard and Storm, 1995). The approach used by Pikul and others (1974) and Refsgaard and Storm (1995) is similar to the approach used in developing the Unsaturated-Zone Flow (UZF1) Package for MODFLOW-2005, which solves the three-dimensional ground-water flow equation using finite-difference techniques (Harbaugh, 2005; fig. 1). The one-dimensional form of Richards’ equation is approximated by a kinematic-wave equation that is solved by the method of characteristics (Smith, 1983). The method of characteristics solution for unsaturated flow precludes the need to develop a structured grid of the unsaturated zone for numerical stability and simplifies handling of the moving boundary defined by the interface between the water table and unsaturated zone.
This report presents a new package for simulating vertical unsaturated flow in MODFLOW-2005 (Harbaugh, 2005). The package is intended to provide an efficient means of simulating recharge in MODFLOW-2005 that considers the effects of flow, ET, and storage in the unsaturated zone; it is also intended to be used for coupling MODFLOW to precipitation-runoff models. The theoretical development of the kinematic-wave approximation to Richards’ equation and the method of characteristic solution was presented by Smith (1983) and Smith and Hebbert (1983). The method of characteristics solution for unsaturated flow is extended in this report to consider ET losses. The method was initially incorporated with MODFLOW-2000 through the simulation of unsaturated flow beneath intermittent streams without considering ET (Niswonger and Prudic, 2004).
This report also describes how the UZF1 Package is coupled to MODFLOW-2005 and how the UZF1 Package calculates ground-water seepage to land surface. A comparison is presented between MODFLOW-2005 using the UZF1 Package and the U.S. Geological Survey (USGS) Variably-Saturated Two-Dimensional Flow and Transport Model (VS2DT; Healy, 1990) for a simple problem that involves vertical unsaturated flow with ET. Two test simulations also are described: the first test simulation shows results from a transient model of a 27 km2 watershed in which infiltration, ET, and ground-water discharge vary through time. The second test simulation is a simple problem that can be used to verify proper code installation and as a template for setting up new problems.
A more complex method for simulating flow through the unsaturated zone is available for MODFLOW-2000. The Variably-Saturated Flow (VSF) Process (Thoms and others, 2006) uses a finite-difference approximation to solve the three-dimensional form of Richards’ equation. VSF replaces the standard Ground-Water Flow (GWF) Process in MODFLOW-2000 (Harbaugh and others, 2000). The process is designed for problems where horizontal flow within the unsaturated zone is important. VSF includes packages that can simulate seepage faces, infiltration with ponding, bare soil evaporation, and plant transpiration. The VSF Process offers a more rigorous and more computationally demanding treatment of flow through the unsaturated zone than that provided by the UZF1 Package.
The U.S. Geological Survey Ground-Water Resources Program and the Office of Ground Water funded this work. The original idea to develop the UZF1 Package for MODFLOW began in the summer of 1995 and was inspired by interest in coupling MODFLOW to a precipitation-runoff model. The development of this work began with many conversations with Jon P. Fenske and Arlen D. Feldman (retired) of the Army Corps of Engineers Hydrologic Engineering Center, Davis, California, and with Stanley A. Leake and Richard W. Healy of the U.S. Geological Survey. The Hydrologic Engineering Center provided the initial support to develop a plan for incorporating precipitation runoff models with MODFLOW (Fenske and Prudic, 1998). The authors are grateful to Steven L. Markstrom of the U.S. Geological Survey National Research Program for his help in the final design of UZF1, and the technical reviewers of this report, including Paul M. Barlow, Randall T. Hanson, Arlen W. Harbaugh, Devin L. Galloway, and Richard W. Healy of the U.S. Geological Survey.
U.S.
Department of the Interior | U.S. Geological
Survey
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